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    <title>gfare</title>
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    <center>Scilab Function</center>
    <div align="right">Last update : April 1993</div>
    <p>
      <b>gfare</b> -  filter Riccati equation</p>
    <h3>
      <font color="blue">Calling Sequence</font>
    </h3>
    <dl>
      <dd>
        <tt>[Z,H]=gfare(Sl)  </tt>
      </dd>
    </dl>
    <h3>
      <font color="blue">Parameters</font>
    </h3>
    <ul>
      <li>
        <tt>
          <b>Sl</b>
        </tt>: linear system (<tt>
          <b>syslin</b>
        </tt> list)</li>
      <li>
        <tt>
          <b>Z</b>
        </tt>: symmetric matrix</li>
      <li>
        <tt>
          <b>H</b>
        </tt>: real matrix</li>
    </ul>
    <h3>
      <font color="blue">Description</font>
    </h3>
    <p>
    Generalized Filter Algebraic Riccati Equation (GFARE).
    <tt>
        <b>Z</b>
      </tt> = solution, <tt>
        <b>H</b>
      </tt> = gain.</p>
    <p>
    The GFARE for <tt>
        <b>Sl=[A,B,C,D]</b>
      </tt> is:</p>
    <pre>

(A-B*D'*Ri*C)*Z+Z*(A-B*D'*Ri*C)'-Z*C'*Ri*C*Z+B*Si*B'=0
   
    </pre>
    <p>
    where <tt>
        <b>S=(eye()+D'*D)</b>
      </tt>, <tt>
        <b>Si=inv(S)</b>
      </tt>, <tt>
        <b>R=(eye()+D*D')</b>
      </tt>, <tt>
        <b>Ri=inv(R)</b>
      </tt>
    and <tt>
        <b>H=-(B*D'+Z*C')*Ri</b>
      </tt> is such that <tt>
        <b>A+H*C</b>
      </tt> is stable.</p>
    <h3>
      <font color="blue">See Also</font>
    </h3>
    <p>
      <a href="gcare.htm">
        <tt>
          <b>gcare</b>
        </tt>
      </a>,&nbsp;&nbsp;</p>
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